keiths is a complete and desperate loser
-
keiths thinks that if you rearrange the sequence of a set like so: {1,3,5,2,7,9,11,4,13,15,17,6,19,21,23,8…}, that it somehow damages my argument. What a total moron you are, keiths. What's the next number after 8, dumbass? The ellipses at the end say keep going as it went before.
And number lines have an accepted sequence.
keiths is just upset because I exposed his ignorance about nested hierarchies
Yes keiths, I am laughing at you, you ignorant ass
keiths thinks that if you rearrange the sequence of a set like so: {1,3,5,2,7,9,11,4,13,15,17,6,19,21,23,8…}, that it somehow damages my argument. What a total moron you are, keiths. What's the next number after 8, dumbass? The ellipses at the end say keep going as it went before.
And number lines have an accepted sequence.
keiths says that when I compare my sets, for example {1,2,3,4,5,6,...} to {2,4,6,8,10,12,14...} that I am comparing finite sets.
I have already been over that, moron. Yes, every time we check we are checking finite sets. And that will happen for infinity- EVERY time we check one set will always be larger than the other. Always and forever.
Infinity is a journey, keiths. If you don't understand what that means ask OlegT. He will educate you on the subject.
In the same thread keiths appears ignorant of the greenhouse effect (GHE). The GHE says that earth radiates IR/ LWR into the atmosphere which gets absorbed by the greenhouse gasses, re-emitted back to earth, rinse and repeat. Elementary school stuff, keiths. However that only happens when the greenhouse gasses (CO2 in this case) are pointed towards earth. I don't understand why that is so difficult to understand
keiths is just upset because I exposed his ignorance about nested hierarchies
Yes keiths, I am laughing at you, you ignorant ass
posted by Joe G @ 3:35 PM
73 Comments:
At 2:50 AM,
Unknown said…
Once again:
Take two sets. IF you can match them up, 1-to-1, such that every element of both sets is matched up to one and only one element of the other set then the sets are the same size. They have to be. If they were different sizes you'd have some unmatched elements.
It doesn't matter the values of the elements, it doesn't matter what order you match them, it doesn't matter how fast you are counting them. IF you can find a 1-to-1 matching then the sets are the same size.
This works for finite and for infinite sets. It works for sets with elements of different types, i.e. numeric and non-numeric values.
If a set can be put into 1-to-1 correspondence with the positive integers then it's said to be countably infinite (because it matches up with infinite set of counting numbers), But that's just a convention. The important part is the 1-to-1 correspondence.
It's not a journey, it's not two trains.
At 10:46 AM,
Joe G said…
The match is between to like number. With infinite sets you can just count the number of elements- no matching required.
Infinity is a journey.
But all of that is moot. Do you agree with keiths that it is OK to scramble the numbers in an infinite set?
At 1:08 PM,
Joe G said…
Or better yet, do you think that even if the numbers are so scrambled that the train could not, because of that, pick up the numbers in order as they appear on the number line, knowing what numbers are needed given the specification of the set?
At 3:54 PM,
Unknown said…
The match is between to like number. With infinite sets you can just count the number of elements- no matching required.
Counting the elements of a set IS putting them into a 1-to-1 correspondence with the positive integers. If you can say which integer matches with which element and no element or integer is unmatched then the sets are the same size.
And if you insist on matching 'like' numbers then you can't compare sets with no numerical values.
Infinity is a journey.
I don't even know what that means. Perhaps you'd care to offer your definition of infinity.
But all of that is moot. Do you agree with keiths that it is OK to scramble the numbers in an infinite set?
I have no idea why he was suggesting such a thing. Scrambling them doesn't change how many there are. AND, IF I can match up the elements of one set 1-to-1 with the elements of another set then the sets must be the same size. That's the important thing.
Or better yet, do you think that even if the numbers are so scrambled that the train could not, because of that, pick up the numbers in order as they appear on the number line, knowing what numbers are needed given the specification of the set?
I'm not exactly sure what you're asking to be honest. But the order of the elements is not the important thing when determining the size of the set. The only thing that matters is what other sets have the same number of elements.
I can exhibit a 1-to-1 matching between the even positive integers and the positive integers; every element of one set is matched with exactly one element of the other set and no element is unmatched. That can only happen if the sets are the same size. It doesn't matter the order you list them, it doesn't matter how quickly you 'count' them, it has nothing to do with a journey or trains. All it has to do with is 1-to-1 correspondence. If you've got a 1-to-1 correspondence then the sets are the same size, if you can't find a 1-to-1 correspondence then . . . you don't know.
Cantor showed you cannot find a 1-to-1 correspondence between the real numbers and the positive integers so those sets must be of different sizes. BUT you can find a 1-to-1 correspondence between the positive integers (the counting numbers) and the: evens, the odds, the multiples of 3, the primes, the rational numbers, the perfect squares and lots of other sets. At the time it was revolutionary stuff and a lot of mathematicians refused to accept it.
Whatever is going on with you and keiths I'll leave up to you to sort out.
At 4:20 PM,
Joe G said…
And if you insist on matching 'like' numbers then you can't compare sets with no numerical values.
The will be finite so we can just count the number of elements
I don't even know what that means.
I know
I have no idea why he was suggesting such a thing.
He's a desperate ass trying his best to misunderstand JoeMath wrt sets
At 4:28 PM,
Unknown said…
The will be finite so we can just count the number of elements
I can easily construct an infinite set of non-numeric values:
{A, B, C . . . X, Y, Z, AA, BB, CC . . . XX, YY, ZZ, AAA, BBB, CCC . . . }
Excel has a different scheme and if you scroll to the right in a new spread sheet you will see it moving past X, Y and Z.
The point of set theory was to come up with a general set of rules and such that didn't depend on sets with numerical elements.
I know
Well, if you can't explain to anyone else then I doubt you'll find many sympathisers.
He's a desperate ass trying his best to misunderstand JoeMath wrt sets
Then why are you bothering? I disagree with you but I do try and explain things the way I see them clearly and carefully.
At 5:11 PM,
Joe G said…
I can easily construct an infinite set of non-numeric values:
Just numbers of a different flavor. My system would make that set, for example, the standard and then compare all like sets to it
It isn't up to me to explain it. It is up to people to get the proper education so they can understand it.
And the reason I bring up what keiths posts is as the title explains- exposing his ignorance and desperation.
At 5:19 PM,
Unknown said…
Just numbers of a different flavor. My system would make that set, for example, the standard and then compare all like sets to it
How would you do that? Show me the method.
It isn't up to me to explain it. It is up to people to get the proper education so they can understand it.
If you are proposing something different what what is accepted then it's up to you to explain it and show how it works. For instance: what is the cardinality of the set I gave as an example?
And the reason I bring up what keiths posts is as the title explains- exposing his ignorance and desperation.
Well, since I haven't read his post on whatever blog it was then I can't say. But I can try to explain what the accepted mathematics means and implies.
At 5:33 PM,
Joe G said…
I already have explained it to you. I won't be doing it again
If you are proposing something different what what is accepted then it's up to you to explain it and show how it works.
I am not proposing something different. Infinity is a journey is NOT my concept
At 5:40 PM,
Unknown said…
I already have explained it to you. I won't be doing it again
If you're happy with no one taking you seriously it's okay with me.
I am not proposing something different. Infinity is a journey is NOT my concept
Whatever that means. If you prefer not to make the concept clearer then . . .
At 12:44 PM,
Joe G said…
If you're happy with no one taking you seriously it's okay with me.
If you are unable to understand simple explanations that is on you
Whatever that means.
Perhaps infinity isn't your thing.
At 1:27 AM,
Unknown said…
If you are unable to understand simple explanations that is on you
I am asking you to explain your statement: Just numbers of a different flavor. My system would make that set, for example, the standard and then compare all like sets to it
You haven't shown how you would do that.
Perhaps infinity isn't your thing.
Or, infinity is NOT a journey.
I'm trying to show you the standard, well-accepted methods for dealing with elementary sets. You think those methods are wrong and that yours are better. It's fair for people to ask you how you would handle certain situations and, if you want people to take your methods seriously, I would expect you to make an effort to explain your techniques.
If we're not sure what you mean and you don't explain yourself then people are just going to disregard what you say, especially if they already have an approach that works well and is consistent.
At 12:45 PM,
Unknown said…
Well I'm sorry you haven't responded to my post as I thought it would have been interesting to pursue the set theory discussion.
I suspect you've got other concerns that need dealing with.
At 1:23 PM,
Joe G said…
Jerad, First things first. If you cannot understand why {1,2,3,4,5,...} has more elements than {2,4,6,8,10,...} then moving on to anything else is a fool's errand.
At 3:56 PM,
Unknown said…
If you cannot understand why {1,2,3,4,5,...} has more elements than {2,4,6,8,10,...} then moving on to anything else is a fool's errand.
IF there were more positive integers than positive even integers then I would be unable to find a way to match up the elements of each set 1-to-1 with elements of the other set. There would always be some elements of the positive integers that had no 'partner' in the positive even integers. But I CAN match up the positive integers with the positive even integers so that no element of either set is unmatched. Give me an element of either set and I can tell you its 'partner' in the other set. That can only happen if the sets have the same number of elements. It doesn't matter how many ways there are of matching up the sets that aren't 1-to-1, what matters is that I can find at least one 1-to-1 matching. And that can only happen between sets of the same size. Clearly.
At 5:37 PM,
Joe G said…
IF there were more positive integers than positive even integers then I would be unable to find a way to match up the elements of each set 1-to-1 with elements of the other set.
That doesn't follow. I would expect all countably infinite sets to posses such an arrangement.
However we can use set subtraction to show that one set has more elements than the other.
We already have a way to match numbers- it is the same as when determining if a set is a subset of another.
At 5:43 PM,
Unknown said…
That doesn't follow. I would expect all countably infinite sets to posses such an arrangement.
Correct which is why they are all the same size.
However we can use set subtraction to show that one set has more elements than the other.
Which means you shouldn't be able to find a 1-to-1 matching. But you can. So . . . set subtraction doesn't work. And it particularly doesn't work if you try and compare sets with unlike elements.
We already have a way to match numbers- it is the same as when determining if a set is a subset of another.
There are no restrictions on how to set up a 1-to-1 matching. If it works it works.
If you can find a 1-to-1 matching between two sets, finite or infinite, then they MUST be the same size. No way around it.
At 7:35 PM,
Joe G said…
Correct which is why they are all the same size.
That doesn't follow
Which means you shouldn't be able to find a 1-to-1 matching.
That doesn't follow
And it particularly doesn't work if you try and compare sets with unlike elements.
First things first. You can't even understand the basics
If you can find a 1-to-1 matching between two sets, finite or infinite, then they MUST be the same size
Just repeating it doesn't make it so.
At 1:42 AM,
Unknown said…
That doesn't follow
All countably infinite sets can be put into 1-to-1 correspondence with the positive integers which means all countably infinite sets are the same size.
That doesn't follow
IF there are more positive integers than positive even integers then you could not find a 1-to-1 correspondence. But you can find a 1-to-1 correspondence which means the two sets are the same times.
First things first. You can't even understand the basics
I'm good I think.
Just repeating it doesn't make it so.
Okay, if you think that there are more positive integers than positive even integers then you should be able to find a positive integer that is not matched to a positive even integer in my 1-to-1 matching. Can you find an unmatched positive integer?
My matching:
positive positive
integers even
integers
1 <-----> 2
2 <-----> 4
3 <-----> 6
4 <-----> 8
etc
Because this is a 1-to-1 correspondence any element you take from one set has a single match in the other set which is only matched to that element.
IF there are more positive integers then you should be able to find a positive integer that has no 'partner' in the positive even integers in my mapping. Can you find an unmatched element in the positive integers?
At 10:17 AM,
Joe G said…
All countably infinite sets can be put into 1-to-1 correspondence with the positive integers which means all countably infinite sets are the same size.
You are insane as all you can do is repeat what is being debated.
IF there are more positive integers than positive even integers then you could not find a 1-to-1 correspondence.
Wrong. I would expect all countably infinite sets to be able to be put in a one-to-one correspondence using some matching function. That function, in turn, tells us the relative cardinalities.
Okay, if you think that there are more positive integers than positive even integers then you should be able to find a positive integer that is not matched to a positive even integer in my 1-to-1 matching.
Your "matching" is bullshit. The 2 matches the 2. The 4 matches the 4- just as when we are determining if a set is a proper subset of another.
Your matching is contrived and my matching is derived.
At 10:19 AM,
Joe G said…
And if there were the same number of elements then set subtraction should be able to demonstrate such a thing. yet set subtraction proves there are more elements in {1,2,3,4,5,...} then there are in {2,4,6,8,10,...}
At 11:31 AM,
Unknown said…
You are insane as all you can do is repeat what is being debated.
Explain to me how two sets can be put into a 1-to-1 correspondence and be different in size. To be different in size there would have to be unmatched elements in one set but there aren't.
Wrong. I would expect all countably infinite sets to be able to be put in a one-to-one correspondence using some matching function. That function, in turn, tells us the relative cardinalities.
If they can be put into a 1-to-1 correspondence then they must be the same size.
Again, if you think there are more positive integers than positive even integers then you have to be able to find a positive integers that is not matched up to an even integers in my mapping. Can you do that?
By the way, you were never able to tell me the relative cardinality of the primes. Another countably infinite set.
Your "matching" is bullshit. The 2 matches the 2. The 4 matches the 4- just as when we are determining if a set is a proper subset of another.
The '2' in the positive integers is matched with the '4' in the positive even integers. The '3' in the positive integers is matched with the '6' in the positive even integers, etc. No element of either set is unmatched, 1-to-1, with an element of the other set. If one set is bigger then there has to be elements that aren't matched because there wouldn't be enough matches in the other set. Can you find an unmatched element? Yes or no?
Your matching is contrived and my matching is derived.
Show me the mathematical set theory definitions of contrived and derived and why they are pertinent to this issue.
I can match the positive even integers to the positive odd integers on a 1-to-1 basis and show those two sets are the same but you cannot use 'set subtraction' to show that.
Can you use your method to find the relative cardinality of the primes? Let's see it.
At 11:47 AM,
Joe G said…
Explain to me how two sets can be put into a 1-to-1 correspondence and be different in size.
It's called a mapping function.
The '2' in the positive integers is matched with the '4' in the positive even integers.
a 2 does not match a 4.
Show me the mathematical set theory definitions of contrived and derived and why they are pertinent to this issue.
Show me why that is required.
I am done with this- set subtraction proves there are more elements in the set {1,2,3,4,5,...} than in {2,4,6,8,10,...}
If what you say is true then that would be impossible.
At 12:22 PM,
Unknown said…
It's called a mapping function.
If I have a 1-to-1 mapping that means each and every element of one set is matched, uniquely to a member of another set. And there is no element of either set unmatched to a unique element of the other set. No element of either set is matched to more than one element of the other set. Explain to me how two sets in a 1-to-1 correspondence can be different in size. It would require there to be at least one element of one of the sets not having a match with an element of the other set. So far you have been unable to find a positive integer that is not matched to a positive even integer in my scheme even though you claim there are more positive integers. Since you can't find an unmatched element the sets must be the same size.
a 2 does not match a 4.
That's how my scheme works. And, so far, you can't find an element of the positive integers that's unmatched with an element of the positive even integers in my scheme.
Show me why that is required.
If you say something that has no mathematical basis when discussing mathematics and you can't specify what you mean then it will be disregarded.
I am done with this- set subtraction proves there are more elements in the set {1,2,3,4,5,...} than in {2,4,6,8,10,...}
Then you should be able to find a positive integer that is unmatched to a positive even integer in my scheme.
If what you say is true then that would be impossible.
I say the sets are the same size, they have the same number of elements, because I have found a way to pair them up so that no element of either set is unpaired. How can that be if one set is bigger? If one set is bigger then there would be at least one unpaired element from one set. But you haven't been able to find one.
If I'm wrong then find an unpaired positive integer in my scheme.
At 2:10 PM,
Joe G said…
If I have a 1-to-1 mapping that means each and every element of one set is matched, uniquely to a member of another set.
Via a mapping function.
I am done with this- set subtraction proves there are more elements in the set {1,2,3,4,5,...} than in {2,4,6,8,10,...}
It isn't my fault that you are too dim to understand that fact
At 4:44 PM,
Unknown said…
Via a mapping function.
So . . . show me an unmatched member of the positive integers under my mapping function.
I keep asking you the same question.
It isn't my fault that you are too dim to understand that fact
And I keep saying: if you are right then there must be some element(s) of the positive integers that have no partner in the positive even integers under my mapping scheme. And yet you haven't come up with such an example.
And you haven't provided the relative cardinality of the primes according to your methods.
You made a claim, I provided a counter example, you haven't been able to contradict my counter example except to assert the same thing over and over again.
Additionally you haven't provided any published mathematical support for you position in particular your use of contrived and derived for mappings. Nor have you provided any work suggesting that some mappings are acceptable or not acceptable.
You might not want to think so but I do support and appreciate people who think outside of the accepted paradigm; folks who challenge the norm. That's sometimes how science progresses. Clearly. But you have to be able to defend your ideas against the accepted material. You have to have better arguments and examples. You have to come up with the goods.
If you insist that the set of positive integers is larger than the set of positive even integers but you you can't tell me how it is that I can partner every element of the positive integers with every element of the positive even integers and have no element of either set unpartnered then . . .
It's pretty clear now: either you can show that there are unpartnered elements of the positive integers under my scheme or you can't. So, can you do that?
At 7:45 PM,
Joe G said…
Wow, you are dense. There aren't any unmatched numbers using your contrived/ unnatural scheme. The word "contrived" has meanings even in math, duh.
That mapping just shows the sets are both countable.
I am done with this- set subtraction proves there are more elements in the set {1,2,3,4,5,...} than in {2,4,6,8,10,...}
It isn't my fault that you are too dim to understand that fact.
And don't talk about science as it is clear that you are ignorant of the subject
At 2:20 AM,
Unknown said…
Wow, you are dense. There aren't any unmatched numbers using your contrived/ unnatural scheme.
Correct. And that can only happen if the sets are the same size.
The word "contrived" has meanings even in math, duh.
Really? References please.
That mapping just shows the sets are both countable.
Correct. And all countably infinite sets are the same size.
I am done with this- set subtraction proves there are more elements in the set {1,2,3,4,5,...} than in {2,4,6,8,10,...}
Nope because then you couldn't put them into a 1-to-1 correspondence. You'd have unpartnered elements which you don't.
It isn't my fault that you are too dim to understand that fact.
It's not a fact because it is inconsistent with the 1-to-1 correspondence that you admit exists.
And don't talk about science as it is clear that you are ignorant of the subject
Whatever.
Anyway, you've admitted there is a 1-to-1 correspondence between the positive integers and the positive even integers which can only happen if the sets are the same size otherwise you'd have unpartnered elements which you don't have.
Your 'set subtraction' is wrong because it gives you a false conclusion.
At 8:43 AM,
Joe G said…
Again all the one-to-one mapping does is show the sets are countable. The fact that a mapping function is needed is also proof the sets are not the same size.
Set subtraction proves there are more elements in {1,2,3,4,5,...) than in {2,4,6,8,10,...}
At 9:33 AM,
Unknown said…
Again all the one-to-one mapping does is show the sets are countable.
If they're both countable and infinite AND you can partner them up so that no elements are left out then they must be the same size. Otherwise something would be left out which is not the case.
The fact that a mapping function is needed is also proof the sets are not the same size.
Really? References please. (Don't worry, I don't expect you to come back with anything, just like you can't explain what 'contrived' means in a mathematical set theory context.)
Set subtraction proves there are more elements in {1,2,3,4,5,...) than in {2,4,6,8,10,...}
Then explain how it is that you can partner-up the elements of both sets so that no element of either set doesn't have a partner from the other set? If they were different sizes then something would be left out but nothing is. You admitted that nothing gets left out so . . .
At 9:46 AM,
Joe G said…
Stop asking me to explain what I have already explained. And if you are too stupid to understand that a mapping function proves the two sets are not the same size then you are too stupid to have this discussion.
The fact remains that set subtraction proves there are more elements in {1,2,3,4,5,...) than in {2,4,6,8,10,...}. And your whining will never change that
At 11:36 AM,
Unknown said…
Stop asking me to explain what I have already explained. And if you are too stupid to understand that a mapping function proves the two sets are not the same size then you are too stupid to have this discussion.
You haven't explained how you can have a 1-to-1 mapping between two sets and have the sets be different sizes. There would have to be some elements unmatched but there aren't any. It has nothing to do with a mapping function. Mapping functions are just ways of expressing 1-to-1 correspondence in this case. In general they don't even have to be mathematical.
The fact remains that set subtraction proves there are more elements in {1,2,3,4,5,...) than in {2,4,6,8,10,...}. And your whining will never change that
It's not whining, the 1-to-1 mapping, which you admit exists, proves that the sets have to be the same size or there would be unmatched elements. Where are the unmatched elements?
Since you can't find any unmatched elements in either set then the sets are the same size. Your 'set subtraction' proves nothing and is contradicted by a procedure which works for finite as well as infinite sets.
And you still haven't found the relative cardinality of the primes? Does that mean the set of primes is the same size as the set of positive integers? Not according to 'set subtraction'. So what is the relative cardinality of the primes. I've been waiting a long time for you to come up with it.
At 10:03 AM,
Joe G said…
The fact remains that set subtraction proves there are more elements in {1,2,3,4,5,...) than in {2,4,6,8,10,...}. And your whining will never change that
Set subtraction found unmatched elements.
And you still haven't found the relative cardinality of the primes?
I say that I have. You choked on it. Big difference
At 3:01 PM,
Unknown said…
Set subtraction found unmatched elements.
Which elements are those then? Which elements of the positive integers are unmatched with the positive even integers in my scheme?
I say that I have. You choked on it. Big difference
Excuse me but you never produced a clear and unambiguous statement about the relative cardinality of the primes. And, if you did, then you should be able to easily prove me incorrect.. Provide a link for the onlookers.
And you should be able to answer the following: is the relative cardinality of the primes more or less than the relative cardinality of the multiples of 29.
Time to step up to the mark.
At 8:34 AM,
Unknown said…
Sorry if I've already replied! I can't remember for sure.
Set subtraction found unmatched elements.
Name one.
I say that I have. You choked on it. Big difference
Well, link to your specific answer then.
At 9:29 AM,
Joe G said…
Set subtraction found that all odd numbers are left unmatched, duh.
As for the primes I have already covered it and seeing that you cannot even understand the basics of set subtraction then you don't have a chance at understanding the primes. Heck even you should be able to do what you ask- but only if you are 1/2 the math person that you think you are.
At 3:25 PM,
Unknown said…
Set subtraction found that all odd numbers are left unmatched, duh.
But you admitted in a previous comment that there were no unmatched elements. And my mapping clearly shows what the odd numbers are matched to.
If you give me an element of the positive integers I will be able to tell you what element of the positive even intergers it is mapped to. If you think that there are more positive integers than positive even integers then you should be able to find a positive integer that has no partner in the positive even integers in my scheme. And you've yet to find one.
As for the primes I have already covered it and seeing that you cannot even understand the basics of set subtraction then you don't have a chance at understanding the primes. Heck even you should be able to do what you ask- but only if you are 1/2 the math person that you think you are.
If you have figured out the specific relative cardinality of the primes then all you need to do is to link to that explanation or repeat it. You're the one who's making the claim, you're the one who needs to support it. If you can.
At 8:42 PM,
Joe G said…
But you admitted in a previous comment that there were no unmatched elements
I have always said that set subtraction proves there are unmatched elements. I have also always said that a mapping function can put elements in a one-to-one correspondence which only proves the sets are countable.
Natural matching shows there are unmatched elements.
If you have figured out the specific relative cardinality of the primes then all you need to do is to link to that explanation or repeat it.
You should be able to do it.
At 2:03 AM,
Unknown said…
I have always said that set subtraction proves there are unmatched elements.
But you can't find any in my scheme.
I have also always said that a mapping function can put elements in a one-to-one correspondence which only proves the sets are countable.
If you can match up the elements of two sets, 1-to-1, so that no element of either set is unmatched with an element of the other set then the sets must be the same size. If you think they aren't then it's up to you to find unmatched elements. You claim there are more positive integers than positive even integers but, under my matching scheme, you have been unable to find any unmatched elements.
You are making claims which you can not support.
Natural matching shows there are unmatched elements.
The point is that I can find A matching that is 1-to-1. It doesn't matter how many are not 1-to-1.
You should be able to do it.
You are the one making the claim and clearly you cannot deliver.
Relative cardinality is your idea, I'm under no obligation to attempt to make the idea work. Your argument is starting to sound like the one you make for Dr Dembski's metric: it's you guys fault we can use it.
When you come up with an idea YOU have to make it work. Otherwise no one will consider it. Just like no one uses Dr Dembski's metric and why no one uses your relative cardinalities.
At 9:18 AM,
Joe G said…
If you can match up the elements of two sets, 1-to-1, so that no element of either set is unmatched with an element of the other set then the sets must be the same size.
Not necessarily. If set subtraction shows there are unmatched elements then clearly there is something wrong with your methodology.
The point is that I can find A matching that is 1-to-1.
You can find a MAPPING, not a matching.
Relative cardinality is your idea,
So what? I use other people's ideas in math- so do you. I am under no obligation to satisfy your willful ignorance.
Just like no one uses Dr Dembski's metric and why no one uses your relative cardinalities.
No one uses Dembski' s metric because evolutionary biologists don't have anything to feed the equations. That is because they don't have any science nor evidence.
And no one uses Cantor's concept that all countably infinite sets have the same cardinality. It is a useless claim- meaningless to everyone in the world.
At 11:40 AM,
Unknown said…
Not necessarily. If set subtraction shows there are unmatched elements then clearly there is something wrong with your methodology.
Yet you can't find an unmatched (or mapped) element of either set in my scheme.
You can find a MAPPING, not a matching.
I use the term matching loosely. But I have clearly shown a way to partner elements of both sets in a 1-to-1 mapping so that no element of either set is unmatched or unmapped to an element of the other set.
So what? I use other people's ideas in math- so do you. I am under no obligation to satisfy your willful ignorance.
If you can't defend your claims what difference does it make?
No one uses Dembski' s metric because evolutionary biologists don't have anything to feed the equations. That is because they don't have any science nor evidence.
You gotta love that Dr Dembski came up with a formula he couldn't use. That is pretty funny. So why isn't someone from the ID camp trying to figure out how to evaluate his metric? Wouldn't that be a reasonable bit of research? Not that any ID person is trying to do that mind you.
And no one uses Cantor's concept that all countably infinite sets have the same cardinality. It is a useless claim- meaningless to everyone in the world.
You always say that after you've failed to support one of your claims about relative cardinality.
So what's the relative cardinality of the prime numbers?
And, while you're at it . . . what's the relative cardinality of the real numbers? How about the irrational numbers? How about the transfinite numbers?
Let's see how your relative cardinalities work once you get past the easy stuff. It doesn't matter to me since no one uses the idea for those kind of sets.
At 12:44 PM,
Joe G said…
Yet you can't find an unmatched (or mapped) element of either set in my scheme.
Set subtraction shows there are infinite unmatched elements.
No one uses Dembski' s metric because evolutionary biologists don't have anything to feed the equations. That is because they don't have any science nor evidence.
You gotta love that Dr Dembski came up with a formula he couldn't use
You gotta love evolutionary biologists who make untestable claims and call it settled science.
So why isn't someone from the ID camp trying to figure out how to evaluate his metric?
Umm, it is up to you and yours to support your claims. If we did it you wouldn't believe us, moron.
And no one uses Cantor's concept that all countably infinite sets have the same cardinality. It is a useless claim- meaningless to everyone in the world.
You always say that
It is always true.
Let's see how your relative cardinalities work once you get past the easy stuff.
You can't even grasp the easy stuff.
It doesn't matter to me since no one uses the idea for those kind of sets.
No one uses Cantor's concepts for those kinds of sets. At least my way is consistent.
At 4:27 PM,
Unknown said…
Set subtraction shows there are infinite unmatched elements.
But you can't tell me an unmatched/mapped positive integer in my scheme. Name a positive integer and I'll tell you which positive even integer I'm mapping it to. Name a positive even integer and I'll tell you which positive integer I'm matching it with.
You gotta love evolutionary biologists who make untestable claims and call it settled science.
Too bad for you millions of working biologists disagree with you. AND you still can't compute Dr Dembski's metric. Who comes up with a metric they can't even compute?
Umm, it is up to you and yours to support your claims. If we did it you wouldn't believe us, moron.
Dr Dembski came up with a metric which he couldn't compute. No one in the ID camp is even trying to figure out how to compute it. This has nothing to do with any claim or research on the part of evolutionary biologists. This has to do with Dr Dembski and ID proponents putting faith in something they can't use even though they proposed it. Too funny.
You can't even grasp the easy stuff.
You can't compute the relative cardinality of the primes. You can't compute the relative cardinality of the real numbers. You can't compute the relative cardinality of the transfinite numbers. You can't compute the relative cardinality of the irrational numbers. Maybe you should work on that stuff before you cast aspersions. It is your system after all.
No one uses Cantor's concepts for those kinds of sets. At least my way is consistent.
How is it consistent when you can't compute the things I've just mentioned?
At 9:20 AM,
Joe G said…
Set subtraction shows there are infinite unmatched elements, which proves there is an issue with your "scheme".
Too bad for you millions of working biologists disagree with you.
Too bad for you they cannot refute what I say.
AND you still can't compute Dr Dembski's metric.
What's to compute? Evos have failed to provide anything but dogma.
No one in the ID camp is even trying to figure out how to compute it.
It isn't up to us, asshole. If we did it no one would believe us. Your scientists can't come up with anything- nothing so it isn't our fault, loser.
This has nothing to do with any claim or research on the part of evolutionary biologists.
It has everything to do with evolutionary biologists. Dembski's metric would be moot if they actually had something. But they don't.
You can't compute the relative cardinality of the primes.
Bet me, then. Put up thousands of dollars, I will do the same and then you will lose it.
No one uses Cantor's concepts for those kinds of sets. At least my way is consistent.
How is it consistent when you can't compute the things I've just mentioned?
Your Gish gallop just proves that you are a desperate little imp. There isn't anything that prevents anyone from determining the relative cardinality of primes.
BTW, asswipe, I never said my system works on real numbers, transfinite numbers nor irrational numbers.. My system works for the countably infinite. So perhaps you should pull your head out of your ass and buy a vowel.
At 10:22 AM,
Unknown said…
Set subtraction shows there are infinite unmatched elements, which proves there is an issue with your "scheme".
But you can't find an unmatched positive integer.
Too bad for you they cannot refute what I say.
You can't find a mechanism that guides mutations.
What's to compute? Evos have failed to provide anything but dogma.
We're talking about a formula that Dr Dembski made up and claimed it could be use to determine something. But he couldn't computer it, you can't compute it and no one uses it because they can't. It has nothing to do with what biologists have or have not done. Dr Dembski came up with something that is useless.
It isn't up to us, asshole. If we did it no one would believe us. Your scientists can't come up with anything- nothing so it isn't our fault, loser.
It is up to you. You guys are the ones that hold it up as some kind of measure.
It has everything to do with evolutionary biologists. Dembski's metric would be moot if they actually had something. But they don't.
Who cares since you guys can't use it.
Bet me, then. Put up thousands of dollars, I will do the same and then you will lose it.
There are several prizes worth lots of money for outstanding contributions to mathematics and if you could compute the relative cardinality of the primes then you could very well win one of them. But you can't so . . . .
Your Gish gallop just proves that you are a desperate little imp. There isn't anything that prevents anyone from determining the relative cardinality of primes.
Well do it then.
BTW, asswipe, I never said my system works on real numbers, transfinite numbers nor irrational numbers.. My system works for the countably infinite. So perhaps you should pull your head out of your ass and buy a vowel.
Uh huh. Are you saying the primes are countably infinite? What about the rational numbers? How do you know the real numbers are not countably infinite since you disagree with Cantor's proof?
At 9:11 AM,
Joe G said…
We're talking about a formula that Dr Dembski made up and claimed it could be use to determine something.
You are one ignorant ass, Jerad. The ONLY reason for Dembski's metric is because evolutionary biologists have FAILed to provide any methodology to test their claims.
You and yours have absolutely NOTHING in the way of testable evidence and methodology.
At 9:56 AM,
Unknown said…
You are one ignorant ass, Jerad. The ONLY reason for Dembski's metric is because evolutionary biologists have FAILed to provide any methodology to test their claims.
Dr Dembski says his metric is "the specified complexity of T given H". He laters goes on to illustrate how this could be used to detect design. But he's never really used it nor has anyone else.
So, in an attempt to refute widely accepted evolutionary theory Dr Dembski proposed a measure that no one can use.
That's not a fail by evolutionary biologists. That's a fail by Dr Dembski. He proposed something that is unusable. You claim it's a fail by evolutionary biologists because you don't believe that unguided processes are up to the job and that somehow forced Dr Dembski to come up with something that doesn't work.
Again, if you're going to challenge orthodoxy then you have to support your challenge. Dr Dembski proposed a method of challenge but it doesn't work. Which is why he isn't still publishing anything about it. It was so roundly vilified by biologists (and mathematicians) that he abandoned the whole effort.
So, no one can use his metric to measure complexity. Your design detection rests pretty much on irreducible complexity which is also roundly dismissed. And if your claim to have detected design is false then you have nothing to support any of your claims. You haven't got anything evidence outside of the same ones you've been using for the last decade or more. You haven't found a mechanism that influences mutations. You can't even specify which mutations are random and which are guided.
Which reminds me: you never really how plant and animal breeders could create new varieties according to their whims if there is a mechanism that's trying to influence mutations.
At 11:38 AM,
Joe G said…
You have serious issues. For one there isn't any scientific theory of evolution. For another evolutionary biologists have no clue how to test their claims.
Evolutionary biologists FAIL because they cannot test their claims. Their entire position is unusable.
Challenge orthodoxy? What's to challenge? They don't have anything
Your design detection rests pretty much on irreducible complexity which is also roundly dismissed.
Only dismissed by ignorant cowards. And evolutionists cannot explain it. So fuck poff, loser.
Which reminds me: you never really how plant and animal breeders could create new varieties according to their whims if there is a mechanism that's trying to influence mutations.
Why would that be an issue?
Peer-review is devoid of supporting evidence for unguided evolution. And the paper "waiting for two mutations" says there isn't enough time in the universe for unguided evolution to produce ATP synthase.
All you have is sheer dumb luck and that means you don't have any science
At 4:07 PM,
Unknown said…
You have serious issues. For one there isn't any scientific theory of evolution. For another evolutionary biologists have no clue how to test their claims.
And, again, millions of working biologists disagree with you.
Evolutionary biologists FAIL because they cannot test their claims. Their entire position is unusable.
Belied by the fact that every day research is published regarding evolution via unguided processes.
Challenge orthodoxy? What's to challenge? They don't have anything
Again, the clear and obvious evidence says otherwise.
Only dismissed by ignorant cowards. And evolutionists cannot explain it. So fuck poff, loser.
Whatever. No matter how abusive and dismissive you get that doesn't mean anyone is taking you seriously.
Why would that be an issue?
You think mutations are guided by some undefined and undiscovered mechanism (which James Shapiro has not discovered by the way). IF that is true then you have to explain how breeders were able to create forms based on their preferences which were not necessarily in agreement with your supposed guidance. In other words, IF there is guidance then why doesn't it override human preferences?
Peer-review is devoid of supporting evidence for unguided evolution. And the paper "waiting for two mutations" says there isn't enough time in the universe for unguided evolution to produce ATP synthase.
That 'paper' (was it peer-reviewed?) has been disputed and disregarded. Now you can stamp your feet and deny the counter-arguments but the fact is that all the things you claim support your view are NOT accepted by the vast majority of working biologists.
All you have is sheer dumb luck and that means you don't have any science
Which shows how little you really understand evolutionary theory. And it shows how much you gloss over the fact that all your side has is disputed and unestablished design detection. You do come close to admitting that when you say that all evolutionary biologists have to do is to provide plausible pathways. Which they are in the process of doing. You are being disingenuous though because you'll just claim the mutations were guided with no real evidence that that is the case.
And, guess what, you still haven't found the relative cardinality of the primes! Time to admit you can't do it.
At 9:57 AM,
Joe G said…
And, again, millions of working biologists disagree with you.
And again I don't care as they definitely cannot refute what I post.
Belied by the fact that every day research is published regarding evolution via unguided processes.
Liar
Again, the clear and obvious evidence says otherwise.
Liar
You think mutations are guided by some undefined and undiscovered mechanism (which James Shapiro has not discovered by the way).
Ignorant ass. I have posted mechanisms. YOU don't have a mechanism capable of producing living organisms; eukaryotes; ATP synthase nor any other multi-protein machine.
That 'paper' (was it peer-reviewed?) has been disputed and disregarded.
Liar. It was a well-accepted paper because evoTARDs thought it refuted Behe.
Which shows how little you really understand evolutionary theory.
I know more than you ever will.
You do come close to admitting that when you say that all evolutionary biologists have to do is to provide plausible pathways.
That is another lie. They have to do much more than that, moron.
And, guess what, you still haven't found the relative cardinality of the primes!
Yes, I have found it. You never will because you are too stupid to do so.
At 10:07 AM,
Joe G said…
In other words, IF there is guidance then why doesn't it override human preferences?
Why would it?
At 1:59 AM,
Unknown said…
And again I don't care as they definitely cannot refute what I post.
You can't even support your own claims.
Liar
All evidence to the contrary.
Liar
Repeating a claim doesn't make it true.
gnorant ass. I have posted mechanisms. YOU don't have a mechanism capable of producing living organisms; eukaryotes; ATP synthase nor any other multi-protein machine.
You have NOT posted mechanisms. You can't find the 'extra programming' in cells that guides mutations. You can't demonstrate how mutations are affected by environmental pressures. Dr Shapiro didn't specify a mechanism and you haven't either.
Liar. It was a well-accepted paper because evoTARDs thought it refuted Behe.
Not the same as peer-reviewed is it?
I know more than you ever will.
As demonstrated by your lengthy publication record . . . oh, wait . . . you don't have a publication record. Or a research record. Or a teaching record.
That is another lie. They have to do much more than that, moron.
So you've changed your tune then. Biologists don't just have to provide a plausible, step-by-step pathway . . . now they have to do more? Shifting the goal posts is naughty.
Yes, I have found it. You never will because you are too stupid to do so.
You haven't found the specific relative cardinality of the primes. You keep claiming you have but you can't end the argument by stating what it is. No one is fooled by your obfuscation. Clearly state your results or admit you haven't got any. Bluffing doesn't win in mathematics.
At 10:13 AM,
Joe G said…
You can't even support your own claims.
And yet I have. More so than any evolutionary biologist has supported any claims of unguided evolution.
All evidence to the contrary.
Liar
Repeating a claim doesn't make it true.
And yet that is all that you do
You have NOT posted mechanisms
Liar
As demonstrated by your lengthy publication record . . . oh, wait . . . you don't have a publication record. Or a research record. Or a teaching record.
You are a dick and a little dick at that. None of what you posted means anything to whether or not I understand biology and evolution better than you.
So you've changed your tune then.
No. I never made the claim you attribute to me.
You haven't found the specific relative cardinality of the primes.
Yes, I have.
At 4:52 PM,
Unknown said…
And yet I have. More so than any evolutionary biologist has supported any claims of unguided evolution.
In your many and prolific publications.
Liar
No, you have NOT provided a clear mechanisms by which mutations are guided.
You are a dick and a little dick at that. None of what you posted means anything to whether or not I understand biology and evolution better than you.
You always get abusive when you haven't got evidence to back up your claims.
Yes, I have.
You have NOT determined the relative cardinality of the primes except to make some vague guesses. No one is taking you seriously anymore.
At 9:53 AM,
Joe G said…
No, you have NOT provided a clear mechanisms by which mutations are guided.
Yes, I have.
You have NOT determined the relative cardinality of the primes
Yes, I have.
And I get abusive after you have been abusive. Are you really that much of an asshole, Jerad?
At 4:47 PM,
Unknown said…
Yes, I have.
You have not specified a mechanism in cells which guides mutations.
Yes, I have.
You have not determined (according to your system) the relative cardinality of the primes. Or the relative cardinality of the cubes. Or the relative cardinality of the 4th powers. Nor have you explained how you know that the Reals are not countably infinite since you rejected Cantor's work. Do you think the Rational numbers are countably infinite? Are the irrational numbers countably infinite? How do you know?
And I get abusive after you have been abusive. Are you really that much of an asshole, Jerad?
Defend your claims if you can and stop calling people names.
At 5:41 PM,
Joe G said…
You have not specified a mechanism in cells which guides mutations.
Yes, I have. Your alternative is they just happen just because.
You have not determined (according to your system) the relative cardinality of the primes.
Yes, I have. You cannot show that such a thing is impossible.
Nor have you explained how you know that the Reals are not countably infinite since you rejected Cantor's work.
Don't tell me what I reject you little punk. And don't tell me what my system has to do.
Defend your claims if you can and stop calling people names.
Don't tell me what to do. You can't defend anything and all you can do is call people names and deny
At 3:01 AM,
Unknown said…
Yes, I have. Your alternative is they just happen just because.
Both wrong.
Yes, I have. You cannot show that such a thing is impossible.
I didn't say it was impossible. I am saying you haven't done it. Nor have you stated whether or not the Rationals are countably infinite. AND, if they are, what their relative cardinality is. Nor have you stated how you know that the Reals are not countably infinite.
Don't tell me what I reject you little punk. And don't tell me what my system has to do.
The point is your system can't handle a lot of situations. If you don't care then it's dead.
In mathematics you have to defend your ideas. If you can't then no one will care or build upon it.
At 9:39 AM,
Joe G said…
Both wrong.
Prove it or shut up, coward
I didn't say it was impossible.
Then shut up
I am saying you haven't done it.
You are an ignorant asshole
The point is your system can't handle a lot of situations.
That is your ignorant and cowardly opinion.
In mathematics you have to defend your ideas.
But you are a no one. And no one uses Cantor's notion that all countable and infinite sets have the same cardinality. No one cares about it and no one has built upon it.
At 5:19 PM,
Unknown said…
Then shut up
You have made a claim that you cannot support. You're not really even trying . You're just be belligerent. So, the conclusion is: you have NOT found, in your system, the relative cardinality of the primes. And I will add: you have not shown or decided whether or not the Rational numbers are countably infinite. Nor have you provided an argument for whether or not the Reals are countably infinite.
You are an ignorant asshole
You have not supported your claims.
That is your ignorant and cowardly opinion.
No, that is clear. You cannot address some basic questions of your system.
But you are a no one. And no one uses Cantor's notion that all countable and infinite sets have the same cardinality. No one cares about it and no one has built upon it.
You made some claims which you cannot defend. Deal with those first.
Under your system:
What is the relative cardinality of the primes?
And here are some further questions?
Are the Rational numbers countably infinite? If they are then what is their relative cardinality?
Are the Real numbers countably infinite? How do you know? If there are then what is there relative cardinality?
These are all fair and reasonable question which you do not have an answer for. And if you don't have answers then no one will ever care at all about your system. Because it can't answer some basic questions.
At 3:33 AM,
Unknown said…
You are an ignorant asshole
You have not determine what you would call the relative cardinality of the primes. You have given no evidence that you have done it. You just keep making a claim which you can't support.
Also you haven't decided if the rational numbers are countably infinite and, if you think they are, then what's their relative cardinality? (They are countably infinite by the way.)
You haven't said how you know the real numbers are not countably infinite.
That is your ignorant and cowardly opinion.
It's true. It's very easy for me to come up with examples your system can't handle.
But you are a no one. And no one uses Cantor's notion that all countable and infinite sets have the same cardinality. No one cares about it and no one has built upon it.
In your opinion. But, since you haven't learned much beyond basic mathematics and you can't be bothered to look things up your opinion means nothing.
At 11:09 AM,
Joe G said…
You have made a claim that you cannot support.
Fuck you, loser
So, the conclusion is: you have NOT found, in your system, the relative cardinality of the primes.
That is the "conclusion" of an ignorant coward
You have not determine what you would call the relative cardinality of the primes.
Yes, I have
You haven't said how you know the real numbers are not countably infinite.
Go ahead and show that they are countable of shut up
But you are a no one. And no one uses Cantor's notion that all countable and infinite sets have the same cardinality. No one cares about it and no one has built upon it.
In your opinion.
Nope, that is a fact. If it wasn't you would just post the evidence that refutes it. But you can't because it doesn't exist.
You are just a mouthy coward who can't even think for himself. Does your mommy still change your diaper?
At 4:28 PM,
Unknown said…
That is the "conclusion" of an ignorant coward
That is based on the fact that you haven't been able to produce what you would call the relative cardinality of the primes. You say you have but you never state what it is.
You haven't figured out the relative cardinality of the rational numbers.
Go ahead and show that they are countable of shut up
Cantor proved that the Reals are not countably infinite. Do you agree with his proof?
Nope, that is a fact. If it wasn't you would just post the evidence that refutes it. But you can't because it doesn't exist.
I have, in the past, shown you examples of how Cantor's work is built up but you just denied it all. No one takes you seriously because you don't consider the evidence, especially when it runs counter to your claims.
You are just a mouthy coward who can't even think for himself. Does your mommy still change your diaper?
No, my mother died in 1981, thanks for asking. Of course real people and their feelings mean nothing to you. You just like to abuse people who won't back down from your onslaught of vitriole. And if we give up and walk away because you're so horrid you claim victory. Is that how mathematics is done? You just claim and claim and claim and abuse and abuse and abuse until the other person gives up?
If you've determined the 'relative cardinality' of the primes then state it.
If you've determined the 'relative cardinality' of the rational numbers then state it.
If you've figured out why the real numbers are (or are not) countably infinite then just state it.
No more abuse, put your cards on the table.
.
At 5:08 PM,
Joe G said…
That is based on the fact that you haven't been able to produce what you would call the relative cardinality of the primes.
That is your ignorant opinion.
Cantor proved that the Reals are not countably infinite.
OK then what is your problem?
I have, in the past, shown you examples of how Cantor's work is built up but you just denied it all.
You have NEVER shown that anyone uses the claim that all countably infinite sets have the same cardinality. You always move the goalposts like a little baby.
If you've determined the 'relative cardinality' of the primes then state it.
Or what?
At 2:41 AM,
Unknown said…
That is your ignorant opinion.
No, that is a fact. You have not found or provided the relative cardinality of the primes or the relative cardinality of the rational numbers.
OK then what is your problem?
Do you agree with Cantor's proof that the Real numbers are not countably infinite?
Or what?
No one will take your claim seriously. I don't many people are taking you seriously now anyway. You keep making claims which you cannot support.
At 8:20 PM,
Joe G said…
You have not found or provided the relative cardinality of the primes
Yes, I have. And you aren't anyone to deny me
the relative cardinality of the rational numbers.
I never said I could do that, asshole.
Do you agree with Cantor's proof that the Real numbers are not countably infinite?
Yes
No one will take your claim seriously
No one uses Cantor's concept so clearly no one takes it seriously
At 3:06 AM,
Unknown said…
Yes, I have. And you aren't anyone to deny me
No, you haven't. Just saying you have doesn't cut it.
I never said I could do that, asshole.
The Rational numbers are countably infinite, you said your method applied to countably infinite sets. Can you find the relative cardinality of the Rational numbers?
Yes
That's good then.
No one uses Cantor's concept so clearly no one takes it seriously
You always try and distract from the fact they you haven't been able to back up your claims. You cannot find the relative cardinality of the primes but you're afraid to admit it. And you can't find the relative cardinality of the rational numbers even though they too are countably infinite.
At 3:08 AM,
Unknown said…
Start here if you want to know what work has really been done estimating the 'density' of the primes.
https://en.wikipedia.org/wiki/Prime_number_theorem
At 10:15 AM,
Joe G said…
Jerad, You are an asshole. You do not get to tell me what I have and have not done. I am not answerable to you.
At 1:16 PM,
Unknown said…
Jerad, You are an asshole. You do not get to tell me what I have and have not done. I am not answerable to you.
No, but you clearly can not back up your claims. So they remain claims. Unestablished claims. Which no one is going to take seriously.
Balls in your court.
At 1:18 PM,
Joe G said…
Yes, I can back up my claims. You are just an ignorant troll who clearly doesn't understand mathematics.
Balls in your mouth
At 2:51 PM,
Unknown said…
Yes, I can back up my claims. You are just an ignorant troll who clearly doesn't understand mathematics.
If you can then do so. I promise to give any evidence serious consideration.
At 5:54 PM,
Joe G said…
I am not answerable to you, dipshit. I give my work to people who matter- you don't. But I will tell you what- you try to find it with respect to primes and I will check your work against mine.
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